The Expected Competitive Ratio for Weighted Completion Time Scheduling

Alexander Souza, Angelika Steger
2005 Theory of Computing Systems  
A set of n independent jobs is to be scheduled without preemption on m identical parallel machines. For each job j, a diffuse adversary chooses the distribution F j of the random processing time P j from a certain class of distributions F j . The scheduler is given the expectation µ j = E[P j ], but the actual duration is not known in advance. A positive weight w j is associated with each job j and all jobs are ready for execution at time zero. The scheduler determines a list of the jobs, which
more » ... is then scheduled in a non-preemptive manner. The objective is to minimise the total weighted completion time j w j C j . The performance of an algorithm is measured with respect to the expected competitive ratio max F∈F E[ j w j C j /OPT], where C j denotes the completion time of job j and OPT the offline optimum value. We show a general bound on the expected competitive ratio for list scheduling algorithms, which holds for a class of so-called new-better-than-used processing time distributions. This class includes, among others, the exponential distribution. As a special case, we consider the popular rule weighted shortest expected processing time first (WSEPT) in which jobs are processed according to the nondecreasing µ j /w j ratio. We show that it achieves E[WSEPT/OPT] ≤ 3 − 1/m for exponential distributed processing times.
doi:10.1007/s00224-005-1261-z fatcat:7g4l2tmucfexfbelkkrodlgk64